Simulation of therapeutic electron beam tracking through a non-uniform magnetic field using finite element method.

INTRODUCTION: In radiotherapy, megaelectron volt (MeV) electrons are employed for treatment of superficial cancers. Magnetic fields can be used for deflection and deformation of the electron flow. A magnetic field is composed of non-uniform permanent magnets. The primary electrons are not mono-energetic and completely parallel. Calculation of electron beam deflection requires using complex mathematical methods. In this study, a device was made to apply a magnetic field to an electron beam and the path of electrons was simulated in the magnetic field using finite element method. METHODS: A mini-applicator equipped with two neodymium permanent magnets was designed that enables tuning the distance between magnets. This device was placed in a standard applicator of Varian 2100 CD linear accelerator. The mini-applicator was simulated in CST Studio finite element software. Deflection angle and displacement of the electron beam was calculated after passing through the magnetic field. By determining a 2 to 5cm distance between two poles, various intensities of transverse magnetic field was created. The accelerator head was turned so that the deflected electrons became vertical to the water surface. To measure the displacement of the electron beam, EBT2 GafChromic films were employed. After being exposed, the films were scanned using HP G3010 reflection scanner and their optical density was extracted using programming in MATLAB environment. Displacement of the electron beam was compared with results of simulation after applying the magnetic field. RESULTS: Simulation results of the magnetic field showed good agreement with measured values. Maximum deflection angle for a 12 MeV beam was 32.9° and minimum deflection for 15 MeV was 12.1°. Measurement with the film showed precision of simulation in predicting the amount of displacement in the electron beam. CONCLUSION: A magnetic mini-applicator was made and simulated using finite element method. Deflection angle and displacement of electron beam were calculated. With the method used in this study, a good prediction of the path of high-energy electrons was made before they entered the body.

An Analytical Method to Calculate Phantom Scatter Factor for Photon Beam Accelerators.

INTRODUCTION: One of the important input factors in the commissioning of the radiotherapy treatment planning systems is the phantom scatter factor (Sp) which requires the same collimator opening for all radiation fields. In this study, we have proposed an analytical method to overcome this issue. METHODS: The measurements were performed using Siemens Primus Plus with photon energy 6 MV for field sizes from 5×5cm2 to 40×40cm2. Phantom scatter factor was measured through the division of total scatter output factors (Scp), and collimator scatter factor (Sc). RESULTS: The mean percent difference between the measured and calculated Sp was 1.00% and -3.11% for 5×5, 40×40 cm2 field size respectively. CONCLUSION: This method is applicable especially for small fields used in IMRT which, measuring collimator scatter factor is not reliable due to the lateral electron disequilibrium.

Analytical Consideration of Surface Dose and Kerma for Megavoltage Photon Beams in Clinical Radiation Therapy.

BACKGROUND: In radiation therapy, estimation of surface doses is clinically important. This study aimed to obtain an analytical relationship to determine the skin surface dose, kerma and the depth of maximum dose, with energies of 6 and 18 megavoltage (MV). MATERIALS AND METHODS: To obtain the dose on the surface of skin, using the relationship between dose and kerma and solving differential equations governing the two quantities, a general relationship of dose changes relative to the depth was obtained. By dosimetry all the standard square fields of 5x5cm to 40x40cm, an equation similar to response to differential equations of the dose and kerma were fitted on the measurements for any field size and energy. Applying two conditions: a) equality of the area under dose distribution and kerma changes in versus depth in 6 and 18 MV, b) equality of the kerma and dose at x=dmax and using these results, coefficients of the obtained analytical relationship were determined. By putting the depth of zero in the relation, amount of PDD and kerma on the surface of the skin, could be obtained. RESULTS: Using the MATLAB software, an exponential binomial function with R-Square >0.9953 was determined for any field size and depth in two energy modes 6 and 18MV, the surface PDD and kerma was obtained and both of them increase due to the increase of the field, but they reduce due to increased energy and from the obtained relation, depth of maximum dose can be determined. CONCLUSIONS: Using this analytical formula, one can find the skin surface dose, kerma and thickness of the buildup region.

Determination of an Effective Wedge Angle by Combination of Two Arbitrary Universal Wedge Fields in Radiation Therapy of Cancer Patients with Megavoltage Photon Beams.

BACKGROUND: Wedge filters are commonly used in radiation oncology for eliminating hot spots and creating a uniform dose distribution in optimizing isodose curves in the target volume for clinical aspects. These are some limited standard physical wedges (15°, 30°, 45°, 60°),or creating an arbitrary wedge angle, like motorized wedge or dynamic wedge,... The new formulation is presented by the combination of wedge fields for determining an arbitrary effective wedge angles. The isodose curves also are derived for these wedges. MATERIALS AND METHODS: we performed the dosimetry of Varian Clinac 2100C/D with Scanditronix Wellhofer water blue phantom, CU500E, OmniPro - Accept software and 0.13cc ionization chamber for 6Mv photon beam in depth of 10cm (reference depth) for universal physical wedges (15°, 30°, 45°, and 60°) and reference field 10x10cm2. By combining the isodose curve standard wedge fields with compatible weighting dose for each field, the effective isodose curve is calculated for any wedge angle. RESULTS: The relation between a given effective wedge angle and the weighting of each combining wedge fields was derived. A good agreement was found between the measured and calculated wedge angles and the maximum deviation did not exceed 3°. The difference between the measured and calculated data decreased when the combined wedge angles were closer. The results are in agreement with the motorized single wedge appliance in the literature. CONCLUSIONS: This technique showed that the effective wedge angle that is obtained from this method is adequate for clinical applications and the motorized wedge formalism is a special case of this consideration.

Breast Radiotherapy with Mixed Energy Photons; a Model for Optimal Beam Weighting.

Utilization of high energy photons (>10 MV) with an optimal weight using a mixed energy technique is a practical way to generate a homogenous dose distribution while maintaining adequate target coverage in intact breast radiotherapy. This study represents a model for estimation of this optimal weight for day to day clinical usage. For this purpose, treatment planning computed tomography scans of thirty-three consecutive early stage breast cancer patients following breast conservation surgery were analyzed. After delineation of the breast clinical target volume (CTV) and placing opposed wedge paired isocenteric tangential portals, dosimeteric calculations were conducted and dose volume histograms (DVHs) were generated, first with pure 6 MV photons and then these calculations were repeated ten times with incorporating 18 MV photons (ten percent increase in weight per step) in each individual patient. For each calculation two indexes including maximum dose in the breast CTV (Dmax) and the volume of CTV which covered with 95% Isodose line (VCTV, 95%IDL) were measured according to the DVH data and then normalized values were plotted in a graph. The optimal weight of 18 MV photons was defined as the intersection point of Dmax and VCTV, 95%IDL graphs. For creating a model to predict this optimal weight multiple linear regression analysis was used based on some of the breast and tangential field parameters. The best fitting model for prediction of 18 MV photons optimal weight in breast radiotherapy using mixed energy technique, incorporated chest wall separation plus central lung distance (Adjusted R2=0.776). In conclusion, this study represents a model for the estimation of optimal beam weighting in breast radiotherapy using mixed photon energy technique for routine day to day clinical usage.